Results 41 to 50 of about 31,664 (169)
THE TYPICAL STRUCTURE OF MAXIMAL TRIANGLE-FREE GRAPHS
Forum of Mathematics, Sigma, 2015 Recently, settling a question of Erdős, Balogh, and Petříčková showed that there are at most $2^{n^{2}/8+o(n^{2})}$$n$-vertex maximal triangle-free graphs, matching the previously known lower bound.
JÓZSEF BALOGH +3 more
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Triangle decompositions of planar graphs
Discussiones Mathematicae Graph Theory, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Christina M. Mynhardt +1 more
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The χ-Boundedness of P2∪P3-Free Graphs
Journal of Mathematics, 2022 In the early 1980s, Gyárfás introduced the concept of the χ-bound with χ-binding functions thereby extending the notion of perfectness. There are a number of challenging conjectures about the χ-bound.
Xiao Wang, Donghan Zhang
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On (p, 1)-Total Labelling of Some 1-Planar Graphs
Discussiones Mathematicae Graph Theory, 2021 A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, it is proved that the (p, 1)-total labelling number (p ≥ 2) of every 1-planar graph G is at most Δ(G) + 2p − 2 provided that Δ (G) ≥
Niu Bei, Zhang Xin
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Sufficient Conditions for Graphs to Be k-Connected, Maximally Connected, and Super-Connected
Complexity, 2021 Let G be a connected graph with minimum degree δG and vertex-connectivity κG. The graph G is k-connected if κG≥k, maximally connected if κG=δG, and super-connected if every minimum vertex-cut isolates a vertex of minimum degree. In this paper, we present
Zhen-Mu Hong +3 more
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Eternal domination and clique covering
Electronic Journal of Graph Theory and Applications, 2022 We study the relationship between the eternal domination number of a graph and its clique cove-ring number using both large-scale computation and analytic methods. In doing so, we answer two open questions of Klostermeyer and Mynhardt.
Gary MacGillivray +2 more
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Toughness and Triangle-Free Graphs
Journal of Combinatorial Theory, Series B, 1995 We prove that there exist triangle-free graphs with arbitrarily large toughness, thereby settling a longstanding open question. We also explore the problem of whether there exists a \(t\)-tough, \(n/(t + 1)\)-regular, triangle-free graph on \(n\) vertices for various values of \(t\), and provide a relatively complete answer for small values of \(t\).
Bauer, D. +2 more
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Sufficient conditions for maximally edge-connected and super-edge-connected graphs
Communications in Combinatorics and Optimization, 2017 Let $G$ be a connected graph with minimum degree $\delta$ and edge-connectivity $\lambda$. A graph is maximally edge-connected if $\lambda=\delta$, and it is super-edge-connected if every minimum edge-cut is trivial; that is, if every ...
Lutz Volkmann, Zhen-Mu Hong
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A novel method to construct cospectral graphs based on RT operation [PDF]
AIP AdvancesThis paper presents a new graph operation, RT(G), which is formed by transforming each vertex and edge of the original graph G into a triangle. We analyze the relationship between the signless Laplacian characteristic polynomials of the graph RT(G) and ...
Xiu-Jian Wang +2 more
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On triangles in ‐minor free graphs [PDF]
Journal of Graph Theory, 2017 AbstractWe study graphs where each edge that is incident to a vertex of small degree (of degree at most 7 and 9, respectively) belongs to many triangles (at least 4 and 5, respectively) and show that these graphs contain a complete graph (K6 and K7, respectively) as a minor. The second case settles a problem of Nevo.
Boris Albar, Daniel Gonçalves 0001
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